Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - Review Exercises: 42

Answer

The equation of the tangent is $y=-25x+4.$

Work Step by Step

Product Rule $(f’(x)=(u(x)(v(x))’=u’(x)v(x)+u(x)v’(x))$ $u(x)=(x-4) ;u’(x)=1 $ $v(x)= x^2+6x-1;v’(x)=2x+6 $ $f'(x)=(1)(x^2+6x-1)+(2x+6)(x-4)=3x^2+4x-25.$ $f'(0)=3(0^2)+4(0)-25=-25.$ Equation of tangent: $(y-y_0)=m(x-x_0)$ at point $(x_0, y_0)$ and slope $m$. $(y-4)=-25(x-0)\rightarrow y=-25x+4.$
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